What type of pair is formed by the equations (14x+5y=44) and (7x+3y=23)?
Answer and explanation
Correct answer: Consistent and independent
For the two equations, \(\frac{a_1}{a_2}=\frac{14}{7}=2\) and \(\frac{b_1}{b_2}=\frac{5}{3}\). Since \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\), the two lines intersect at exactly one point, so the pair has a unique solution. Therefore, it is consistent and independent. In a consistent dependent pair, all three corresponding ratios are equal. Exam tip: first compare the ratios of the coefficients of \(x\) and \(y\).
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What is the correct answer to this question?
Consistent and independent
Why is this the correct answer?
For the two equations, \(\frac{a_1}{a_2}=\frac{14}{7}=2\) and \(\frac{b_1}{b_2}=\frac{5}{3}\). Since \(\frac{a_1}{a_2}\ne\frac{b_1}{b_2}\), the two lines intersect at exactly one point, so the pair has a unique solution. Therefore, it is consistent and independent. In a consistent dependent pair, all three corresponding ratios are equal. Exam tip: first compare the ratios of the coefficients of \(x\) and \(y\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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